Finite groups whose maximal subgroups of sylow p-subgroups admit a p-solvable supplement

被引：7

作者：

Qian GuoHua ^{[1
]}

机构：

[1] Changshu Inst Technol, Dept Math, Changshu 215500, Peoples R China

来源：

SCIENCE CHINA-MATHEMATICS | 2013年 / 56卷 / 05期

基金：

中国国家自然科学基金;

关键词：

finite group; p-solvable group; Sylow subgroup; supplement;

D O I：

10.1007/s11425-012-4485-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this note, we show that if every maximal subgroup of a Sylow p-subgroup of a finite group has a p-solvable supplement then the group is necessarily p-solvable. This gives a positive answer to Problem 17.111 of the Kourovka Notebook (Unsolved Problems in Group Theory), which was posed by Skiba.

引用

页码：1015 / 1018

页数：4